Quantum dynamics is a versatile tool to understand microscopic phenomena such as atomic collisions, vibrational dynamics or chemical reactions of molecules, heat and electron transfer in nanodevices or biomolecules, etc. Compared to classical dynamics simulations, however, there is no general methods to simulate quantum dynamics, which prevents us from gaining full access to complex quantum phenomena. Here we discuss our recent attempts to reveal complex and dynamical quantum phenomena by using a novel perturbation technique: the examples are quantum chaotic systems (coupled kicked top) and biomolecules. We also improve our theory by extending state space in a systematic way and by including the effect of a fluctuating environment, which is applied to biomolecular systems. Finally we consider an optimal control problem of quantum dynamics. If a quantum system is complex enough such as described by a random matrix, it is shown that there exists an analytic exteral field which can steer a quantum state in the system to any desirable state with a minimal power.